Question: Simplify; express your answer in exponential form. Assume $x\neq 0, a\neq 0$. $\dfrac{{(x^{5})^{2}}}{{(x^{-5}a^{4})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{5}}$ to the exponent ${2}$ . Now ${5 \times 2 = 10}$ , so ${(x^{5})^{2} = x^{10}}$ In the denominator, we can use the distributive property of exponents. ${(x^{-5}a^{4})^{2} = (x^{-5})^{2}(a^{4})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x^{5})^{2}}}{{(x^{-5}a^{4})^{2}}} = \dfrac{{x^{10}}}{{x^{-10}a^{8}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{10}}}{{x^{-10}a^{8}}} = \dfrac{{x^{10}}}{{x^{-10}}} \cdot \dfrac{{1}}{{a^{8}}} = x^{{10} - {(-10)}} \cdot a^{- {8}} = x^{20}a^{-8}$.